1. Calculate the average force per nail when Sarah, who weighs 120 pounds, lies on a bed of nails and is supported by 600 nails.
2. Suppose that you balance a 5-kg ball on the tip of your finger, which has an area of 1 cm2. Show that the pressure on your finger is 50 N/cm2, which is 500 kPa.
3. A 6-kg piece of metal displaces 1 L of water when sub-merged. Show that its density is 6000 kg/m3. How does this compare with the density of water?
4. A dike in Holland springs a leak through a hole of area 1 cm2 at a depth of 2 m below the water surface. How much force must a boy apply to the hole with his thumb to stop the leak? Could he do it?
5. In lab you find that a 1-kg rock suspended above water weighs 10 N. When the rock is suspended beneath the surface of the water, the scale reads 8 N.
a. What is the buoyant force on the rock?
b. If the container of water weighs 10 N on the weighing scale, what is the scale reading when the rock is suspended beneath the surface of the water?
c. What is the scale reading when the rock is released and rests at the bottom of the container?
6. A merchant in Katmandu sells you a solid gold 1-kg statue for a very reasonable price. When you get home, you wonder whether or not you got a bargain, so you lower the statue into a container of water and measure the volume of displaced water. Show that, for pure gold, the volume of water displaced will be 51.8 cm3.
7. In the sketch, the small hydraulic piston has a diameter of 2 cm. The large piston has a diameter of 6 cm. For each Newton of force applied to the small piston, how many Newton's of force are exerted by the large piston?
8. Your friend of mass 100 kg can just barely float in fresh-water. Calculate her approximate volume.